Examples: Al2(SO4)3 Al 2 x 27.0 = S 3 x 32.1 = O 12 x 16.0 = NiSO3 6H2O Ni 1 x 58.7 = S 1 x 32.1 = O 3 x 16.0 = H2O 6 x 18.0 =

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1 Moles Conversion factor: a fraction, equal to one, used to change one unit into another. A conversion factor is formed from an equality! Example: 12 inches = 1 foot 12 in or 1 ft 1 ft 12 in Dimensional Analysis: a problem-solving method using conversion factors also known as factor-label method, picket fence method, or ladder method. Examples: $ nickels $25 4 quarters 5 nickels = 500 nickels $1 1 quarter miles inches 2.5 miles 5280 ft 12 in = in 1 mile 1 ft cm km 125 cm 1 m 1 km = km 100 cm 1000 m m/s miles/hr (mph) 9.76 m 1 km 0.62 miles 60 s 60 min = 21.6 miles s 1000 m 1 km 1 min 1 hr hr Formula Mass: the sum of the average atomic masses of all the atoms present in a chemical formula. There are synonyms based upon the type of compound! Ionic compounds formula mass Molecular compounds molecular mass Elements atomic mass Examples: Al2(SO4)3 Al 2 x 27.0 = S 3 x 32.1 = O 12 x 16.0 = NiSO3 6H2O Ni 1 x 58.7 = S 1 x 32.1 = O 3 x 16.0 = H2O 6 x 18.0 = C6H12O6 C 6 x 12.0 = H 12 x 1.0 = O 6 x 16.0 = amu amu amu Chip Shea 1 3/16/2019

2 Percent composition: the percent, by mass, of each element in a compound. Example: Find the % composition of Al2(SO4)3 (see work for formula mass above!) Al 54.0 amu x 100% = % Al amu S 96.3 amu x 100% = % S amu O amu x 100% = % O amu 100.0% Find the % composition of NiSO3 6H2O (see work for formula mass above!) Ni 58.7 amu x 100% = % Ni amu S 32.1 amu x 100% = % S amu O 48.0 amu x 100% = % O amu H2O amu x 100% = % H2O amu 100.0% Mole conversions Avogadro s Hypothesis: Equal volumes of gases at the same temperature and pressure have equal numbers of particles. Avogadro s number: x This is the number of particles (atoms, molecules, formula units, ions) in one mole of a substance. Mole: the amount of a substance that contains as many particles as are in 12.00g of carbon-12. Molar mass: the mass in grams of one mole of a substance (Equal to the formula mass in grams instead of amu) Molar volume: the volume occupied by one mole of a gas at STP (0 C, 1 atm) = 22.4 L. Conversions with moles: since the mole is a number, it can be used to relate mass (or volume) with the large number of particles that make up that mass (or volume) Particles to moles: particles = moles 6.02 x Example: Convert 4.52 x atoms Au to moles 4.52 x particles Au = moles Au 6.02 x Chip Shea 2 3/16/2019

3 Moles to particles moles 6.02 x = particles Example: Convert 10.5 moles Au to particles 10.5 moles Au 6.02 x = particles Au Grams to moles grams = moles grams Example: Convert 245.7g Au to moles 245.7g Au = moles Au g Au Moles to Grams moles grams = grams Example: Convert moles Au to grams moles Au g g Au s Au Liters to moles liters = moles 22.4 L Example: Convert 495L O2 to liters 495L O2 = moles O2 22.4L O2 Moles to liters moles 22.4 L = liters Example: Convert 10.0 moles O2 to liters 10.0 moles O L = L O2 Particles to grams particles grams = grams 6.02 x Example: Convert 4.52 x particles Au to grams 4.52 x particles g Au = grams Au 6.02 x Chip Shea 3 3/16/2019

4 Grams to particles grams 6.02 x = particles grams Example: Convert 2259g Au to particles 2259g Au 6.02 x = particles Au g Au Determining Empirical and Molecular Formulas Empirical Formula: the simplest formula with the smallest whole number ratio of elements. (Remember: an ionic compound is an empirical formula (f.u.!), but a molecular compound may not be!) Example: CH Molecular formula: the actual formula, often a multiple of the empirical formula. Example: C6H6 (note: NOT an empirical formula!) Calculating Empirical Formulas An empirical formula may be calculated from mass data or percent composition data. Step 1: Convert grams to moles Step 2: Divide each by the smallest number (Step 3: Rationalize to 1 if necessary!) Step 4: Write the empirical formula Examples: Calculate the empirical formula of 2.50g of a compound containing 0.90g Ca and 1.60g Cl. Ca 0.90g Ca = mol Ca 40.1g Ca Cl 1.60g Cl = mol Cl 35.5g Cl Ca mol = Cl mol = CaCl2. No Step 3! Chip Shea 4 3/16/2019

5 Calculate the empirical formula of 13.69g of a compound containing 2.16g of aluminum, 3.85g of sulfur, and 7.68g of oxygen. Al 2.16g Al = mol Al 27.0g Al S 3.85g S = mol S 32.1g S O 7.68g O = mol O 16.0g O Al mol = S mol = Go to Step 3! O mol = Step 3: Gotta do it! Al = x = S = x = O = x = which simplifies to What is the empirical formula of a compound that is 66.0% Ca and 34.0% P? Ca 66.0g Ca = mol Ca 40.1g Ca P 34.0g Cl = mol P 31.0g P Steps 2 and 3: divide each by the smallest number of moles and rationalize Ca mol = x = The empirical formula is P mol = x = Chip Shea 5 3/16/2019

6 Determining Molecular Formulas: A molecular formula may be calculated from an empirical formula and molecular mass. The molecular formula is a whole-number multiple of the empirical formula. Step 1: Convert grams to moles Step 2: Divide each by the smallest number (Step 3: Rationalize to 1 if necessary!) Step 4: Write the empirical formula Step 5: Find the mass of the empirical formula Step 6: Step 7: Divide the molecular mass by the empirical mass Multiply each element in the empirical formula the result of Step 6 Example: Calculate the molecular formula of a compound whose molar mass is 150. g/mol and has a composition of 40.0% C, 6.67% H, and 53.3% O C 40.0g C = 3.33 mol C 12.0 g C H 6.67g H = 6.67 mol H 1.0 g H O 53.3g O = 3.33 mol O 16.0 g O Step 2, 4, and 5: divide each by the smallest number of moles C 3.33 mol = H 6.67 mol = O 3.33 mol = CH2O. The empirical formula mass is 30.0 g/mol. Step 6 and g/mol = g/mol CH2O. The molecular formula is C5H10O5. Chip Shea 6 3/16/2019

7 Determining the Formula of a Hydrate The formula of a hydrated ionic compound may be found using the same basic steps. Example: A g sample of hydrated BaI2 is heated. The anhydrous mass is 9.520g. What is the formula for the hydrate? BaI g BaI2 = mol BaI g BaI2 H2O 0.887g H2O = mol H2O 18.0g H2O BaI mol = 1 The formula for the hydrate is H2O mol = BaI2 2H2O. Example: A sample of hydrated MgSO4 is found to be 48.9% anhydrous salt. What is the formula for the hydrate? MgSO4 48.9g MgSO4 = mol MgSO g MgSO4 H2O 51.1g H2O = mol H2O 18.0g H2O MgSO4 mol = The formula for the hydrate is H2O mol = Chip Shea 7 3/16/2019

CHAPTER 11. The Mole. Mole. One mole of = 6.02 x 10 = 6.02 x 10 CaCl = 6.02 x x 10. Representative Particle. molecules, or formula units

CHAPTER 11. The Mole. Mole. One mole of = 6.02 x 10 = 6.02 x 10 CaCl = 6.02 x x 10. Representative Particle. molecules, or formula units CHAPTER 11 The Mole 11.1 The Mole: Measurement of Matter Matter is measured in one of three ways: (How many?) Mole SI unit that measures the amount of a substance 6.02 x 10 particles of that substance.